This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A229277 #18 Jul 01 2023 15:57:54
%S A229277 0,3,15,63,243,891,3159,10935,37179,124659,413343,1358127,4428675,
%T A229277 14348907,46235367,148272039,473513931,1506635235,4778186031,
%U A229277 15109399071,47652720147,149931729243,470715894135,1474909801623,4613015762523,14403906360531,44906296300479
%N A229277 Number of ascending runs in {1,...,3}^n.
%H A229277 Alois P. Heinz, <a href="/A229277/b229277.txt">Table of n, a(n) for n = 0..1000</a>
%H A229277 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-9).
%F A229277 G.f.: -3*(x-1)*x/(3*x-1)^2.
%F A229277 a(n) = 3^(n-1)*(2*n+1) for n>0, a(0) = 0.
%F A229277 a(n) = 3*A081038(n-1) for n>0.
%F A229277 From _Amiram Eldar_, May 17 2022: (Start)
%F A229277 Sum_{n>=1} 1/a(n) = 3*(sqrt(3)*arctanh(1/sqrt(3)) - 1).
%F A229277 Sum_{n>=1} (-1)^(n+1)/a(n) = 3 - sqrt(3)*Pi/2. (End)
%p A229277 a:= n-> `if`(n=0, 0, 3^(n-1)*(2*n+1)):
%p A229277 seq(a(n), n=0..30);
%t A229277 a[0] = 0; a[n_] := 3^(n - 1)*(2*n + 1); Array[a, 30, 0] (* _Amiram Eldar_, May 17 2022 *)
%Y A229277 Column k=3 of A229079.
%Y A229277 Cf. A081038.
%K A229277 nonn,easy
%O A229277 0,2
%A A229277 _Alois P. Heinz_, Sep 18 2013